The current paper provides an overview of treatment noncompliance at various points in the treatment pathway, especially with respect to treatment for Pelvic-floor Dysfunction. The effects of noncompliance on healthcare are considered, and examples of supporting patients psychologically to increase compliance are discussed. An outline of a method to identify costs of non-compliance, and where such costs most intensely impact the healthcare system, is provided. It is suggested that psychological support is effective in terms of increased compliance and improved healthcare (...) economics. The model is presented for PFD, but the principles developed can be generalised to many aspects of healthcare. (shrink)

To a greater extent than in other technical domains, research and progress in Artificial Intelligence has always been entwined with the fictional. Its language echoes strongly with other forms of cultural narratives, such as fairytales, myth and religion. In this essay we present varied examples that illustrate how these analogies have guided not only readings of the AI enterprise by commentators outside the community but also inspired AI researchers themselves. Owing to their influence, we pay particular attention to the similarities (...) between religious language and the way in which the potential advent of greater than human intelligence is presented contemporarily. We then move on to the role that fiction, science fiction most of all, has historically played and is still playing in the discussion of AI by influencing researchers and the public, shifting the weights of different scenarios in our collectively perceived probability space. We sum up by arguing that the lore surrounding AI research, ancient and modern, points to the ancestral and shared human motivations that drive researchers in their pursuit and fascinate humanity at large. These points of narrative entanglement where AI meets the wider culture should serve to amplify the call to engage ourselves with the discussion of the potential destination of this technology. (shrink)

Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists, and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...) assess several different criteria for individuating and formally representing agents’ choice options. (shrink)

The critics of rational choice theory (RCT) frequently build on the contrast between so-called thick and thin applications of RCT to argue that thin RCT lacks the potential to explain the choices of real-world agents. In this paper, I draw on often-cited RCT applications in several decision sciences to demonstrate that despite this prominent critique there are at least two different senses in which thin RCT can explain real-world agents’ choices. I then defend this thesis against the most influential objections (...) put forward by the critics of RCT. In doing so, I explicate the implications of my thesis for the ongoing philosophical debate concerning the explanatory potential of RCT and the comparative merits of widely endorsed accounts of explanation. (shrink)

Over the last few decades, there have been intense debates concerning the effects of markets on the morality of individuals’ behaviour. On the one hand, several authors argue that markets’ ongoing expansion tends to undermine individuals’ intentions for mutual benefit and virtuous character traits and actions. On the other hand, leading economists and philosophers characterize markets as a domain of intentional cooperation for mutual benefit that promotes many of the character traits and actions that traditional virtue ethics accounts classify as (...) virtuous. In this paper, I join this debate and argue for three claims of general interest to philosophers, economists and policy makers. First, market transactions do not reliably promote individuals’ intentions for mutual benefit, and often select against such intentions. Second, the set of so-called market virtues lacks a substantial overlap with the set of character traits that traditional virtue ethics accounts classify as virtuous. And third, many seemingly virtuous actions observed in market contexts are merely actions in accordance with virtue rather than genuine actions from virtue. These three claims do not license opposition to markets, but challenge the main empirical and theoretical presuppositions of leading virtue ethics defences of markets. (shrink)

According to ‘Strong Composition as Identity’, if an entity is composed of a plurality of entities, it is identical to them. As it has been argued in the literature, SCAI appears to give rise to some serious problems which seem to suggest that SCAI-theorists should take their plural quantifier to be governed by some ‘weak’ plural comprehension principle and, thus, ‘exclude’ some kinds of pluralities from their plural ontology. The aim of this paper is to argue that, contrary to what (...) may appear at first sight, the assumption of a weak plural comprehension principle is perfectly compatible with plural logic and the common uses of plural quantification. As I aim to show, SCAI-theorists can simply claim that their theory must be understood as formulated by means of the most ‘joint-carving’ plural quantifier, thus leaving open the possibility of other, less joint-carving, ‘unrestricted’ plural quantifiers. In the final part of the paper I will also suggest that SCAI-theorists should not only allow for singular quantification over pluralities of entities, but also for plural quantification over ‘super-pluralities’ of entities. (shrink)

Contemporary scholarship concerning science diplomacy is increasingly taking a historical approach. In our introduction to this special issue, we argue that this approach promises insight into science diplomacy because of the tools historians of science bring to their work. In particular, we observe that not only are historians of science currently poised to chart the diplomatic aspects involved in the transnational circulation of technoscientific knowledge, materials, and expertise. They are ready to bring critical global analysis to an important phenomenon that (...) has too often been treated as a benign diplomacy device deployed by the Global North without equal reference to the Global South. Through cases discussed in the articles of the special issue, however, we see that historically, in the Global South as well as the Global North, science diplomacy has often functioned to mediate the circulation of technoscientific knowledge and materials, and its historical study helps to better illuminate the resulting knowledge-power nexus. (shrink)

This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as (...) a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics. (shrink)

This book offers a new reading of Aquinas' views on faith. The author argues that the theological nature of faith is crucial to Aquinas' thought, and that it gives rise to a peculiar and otherwise incomprehensible relationship with reason. The first part of the book examines various modern and contemporary accounts of the relationship between faith and reason in Aquinas' thought. The author shows that these accounts are unconvincing because they exhibit what he calls a Lockean view of faith and (...) reason, which maintains that the relationship in question should only be treated by way of evidence. In other words, this view ignores the specific nature of the Christian faith and the equally specific way it needs to relate to reason. The second part offers a comprehensive account of Aquinas' view of faith. It focuses on the way the divine grace and charity shape the relationship between evidence and human will. The final part of the book ties these ideas together to show how Christian faith, with its specifically theological nature, is perfectly compatible with rational debates. It also argues that employing the specificity of faith may constitute the best way to promote autonomous and successful rational investigations. Aquinas on Faith, Reason, and Charity will be of interest to scholars and advanced students working on Aquinas, philosophy of religion, Christian theology, and medieval philosophy. (shrink)

In the standard Okishio-Morishima approach, the existence of profits is proved to be equivalent to the exploitation of labor. Yet, it can also be proved that the existence of profits is equivalent to the “exploitation” of any good. Labor and commodity exploitation are just different numerical representations of the productiveness of the economy. This paper presents an alternative approach to exploitation theory which is related to the “New Interpretation” (Duménil 1980; Foley 1982). In this approach, labor exploitation captures unequal social (...) relations among producers. The equivalence between the existence of profits and labor exploitation holds, whereas it is proved that there is no relation between profits and commodity “exploitation.”. (shrink)

In recent years, several authors advocated neuroscience imperialism, an instance of scientific imperialism whereby neuroscience methods and findings are systematically applied to model and explain phenomena investigated by other disciplines. Calls for neuroscience imperialism target a wide range of disciplines, including psychology, economics, and philosophy. To date, however, neuroscience imperialism has not received detailed attention by philosophers, and the debate concerning its identification and normative assessment is relatively underdeveloped. In this paper, I aim to remedy this situation by making some (...) conceptual distinctions about neuroscience imperialism and by providing a normative assessment of prominent calls in its favour. I shall articulate and defend two interrelated claims that, I argue, undermine prominent calls for neuroscience imperialism. First, the proponents of neuroscience imperialism significantly overstate the evidential and explanatory relevance of neuroscience methods and findings for the disciplines they target. And second, prominent calls for neuroscience imperialism point to an untenable reductionist position, which rests on unsupported empirical and normative presuppositions. To substantiate these two claims, I shall draw on two sets of influential calls for neuroscience imperialism, which respectively target the economic modelling of choice and entrenched philosophical conceptions of free agency. (shrink)

and in Sect. 5 should be reformulated as follows.

In Christianity, Otherization and Contemporary Politics, Roberto E. Alejandro argues that the identity politics of the American far-left follow an identity paradigm established by early Christian thinkers, and warns that such politics may incline towards the same violence Christianity succumbed to once imbued with political power.

In The Crucifixion and Resurrection of Freddie Gray, Roberto E. Alejandro argues that confessional commitments related to race, society, and structure dominated the interpretation of Gray’s death, stripping the man and his significance from a grieving, impoverished community.

Alessandro Torza argues that Ted Sider’s Lewisian argument against vague existence is insufficient to rule out the possibility of what he calls ‘super-vague existence’, that is the idea that existence is higher-order vague, for all orders. In this chapter it is argued that the possibility of super-vague existence is ineffective against the conclusion of Sider’s argument since super-vague existence cannot be consistently claimed to be a kind of linguistic vagueness. Torza’s idea of super-vague existence seems to be better suited to (...) model vague existence under the assumption that vague existence is instead a form of ontic indeterminacy, contra what Ted Sider and David Lewis assume. (shrink)

Volume 19, Issue 9, September 2019, Page 37-39.

Alejandro offers a theoretical reflection on citizenship as a political category that could make possible a collective identity defined by the citizens' interpretations of traditions and their participation in the public sphere as well as their construction of a hermeneutic historical consciousness. This reflection seeks to pave the way for a vision of citizenship as a space of fluid boundaries within which there is room for diverse and even conflicting understandings of individuality, community, and public identity. Paper edition (unseen), $17.95. (...) Annotation c. by Book News, Inc., Portland, Or. (shrink)

Most discussions of Rawls’s philosophy tend to neglect the strong communitarian strand of his theory: so much so that in the debate between liberals and communitarians Rawls’s account of community has been for the most part intriguingly absent. This article is an attempt to fill in the gap by offering a discussion of the Rawlsian understanding of community as it was presented inA Theory of Justiceand its possible implications for a pluralist society. At the same time, I want to take (...) issue with one of the most influential critiques leveled against Rawls’s conception of the self: namely, Sandel’s critique of the ‘individuated subject’ that, in his view, underlies justice as fairness. Rawls’s constructions, so Sandel argues, rest on an unencumbered self that is individuated in advance and whose identity is fixed once and for all. (shrink)

This study documents how people who inject drugs in rural Puerto Rico perceive payments for participating in HIV epidemiological studies. In-depth interviews were conducted among a subset of active PWID older than 18 years of age who had been previously enrolled in a much larger study. Findings suggest that financial compensation was the main motivation for initially enrolling in the parent study. Then, as trust in the researchers developed, participants came to perceive compensation as part of a reciprocal exchange in (...) which they assisted researchers by providing a trustful account of their experiences and researchers reciprocated with financial support. (shrink)

The pattern of universality and redemption capsizes in the realm of politics. This chapter discusses the relationship of hermeneutics and politics in light of several moments in Western culture and philosophy. It bases this inquiry on Hans‐Georg Gadamer's ideas of hermeneutics, and begins with a discussion of his ontological commitments in order to assess their bearing on the question of politics. Gadamer sees agreement as the ontological outcome of conversations because it is antecedent to the conversation as well as its (...) only goal. Tradition is the source of questions, the tribunal that stipulates the criteria that will validate claims. If we accept that power and the concepts it uses possess both the weight of a dominant reasoning and its criteria to validate claims, then the characterization of politics carries with it the question of tradition and all its potentialities and concomitant problems. (shrink)

Two significant aspects of Thomas Reid's thought seem to be irreconcilable with one another. On the one hand, Reid constantly refers to the substantive benefits which human knowledge receives from the Christian revelation. On the other hand, he does not justify philosophical or scientific beliefs by way of appeal to God. In this essay, I argue that a closer inspection of both Reid's philosophical reflection and scientific investigations shows that the two aspects just mentioned are compatible with one another. In (...) short, although an influence on rational investigation is somehow exerted by divine revelation, this does not limit the autonomy of reason, which is actually stimulated and promoted precisely because of a religiously rooted confidence in our rational faculties. (shrink)

Resumo: As contribuições dos pensadores medievais para o debate em torno da escravidão ainda são pouco conhecidas em seus detalhes. Junto com as abordagens na filosofia antiga, na patrística, no direito romano e no direito canônico, elas formam um corpo de textos e de ideias fundamental para se compreender o tratamento da escravidão do século XVI ao século XIX. Neste artigo, busca-se expor e analisar a abordagem que João Duns Scotus dá ao tema, contrastando-a com as visões de Aristóteles e (...) de Tomás de Aquino. As posições de Scotus dependem de seus pareceres sobre a liberdade, a propriedade e a lei positiva, bem como sobre o significado do livre-arbítrio como condição prático-racional de todos os seres humanos. Na base dessas ideias, Scotus restringe de forma severa as condições de lei positiva segundo as quais a servidão pode ser introduzida com justiça e o escopo de perda de liberdade que pode ser aceito no contrato da escravidão.: The contributions by medieval thinkers to the debate on slavery are still little known in their details. Together with the approaches in ancient philosophy, patristics, Roman law, and Canon law, they constitute a body of texts and ideas that are fundamental to understanding the treatment of slavery from the 16th to the 19th centuries. In this article, we examine John Duns Scotus’ account of the theme, contrasting it with the views of Aristotle and Thomas Aquinas. The position of Scotus depends on his views about freedom, property, and positive law, as well on the meaning of free will as a practical-rational condition of all human beings. Based on these ideas, Scotus severely restricts the conditions of positive law according to which servitude can be justly introduced, and the scope of the loss of freedom that can be accepted in the contract of slavery. (shrink)

The volume offers an overview of current research in ontology, distinguishing basic conceptual issues, domain applications, general frameworks, and mathematical ...

The book is divided into three parts. The first, containing three papers, focuses on the characterization of the central tenets of previii sentism (by Neil McKinnon) and eternalism (by Samuel Baron and Kristie Miller), and on the ‘sceptical stance’ (by Ulrich Meyer), a view to the effect that there is no substantial difference between presentism and eternalism. The second and main section of the book contains three pairs of papers that bring the main problems with presentism to the fore and (...) outlines its defence strategy. Each pair of papers in this section can be read as a discussion between presentists and eternalists, wherein each directly responds to the arguments and objections offered by the other. This is a discussion that is sometimes absent in the literature, or which is at best carried out in a fragmented way. The first two papers of the section deal with the problem of the compatibility of Special Relativity Theory (SRT) and presentism. SRT is often considered to be a theory that contradicts the main tenet of presentism, thereby rendering presentism at odds with one of our most solid scientific theories. Christian Wüthrich’s paper presents arguments for the incompatibility of the two theories (SRT and presentism) within a new framework that includes a discussion of further complications arising from the theory of Qauantum Mechanics. Jonathan Lowe’s paper, by contrast, develops new general arguments against the incompatibility thesis and replies to Wüthrich’s paper. The second pair of papers focuses on the problem that presentists face, in providing grounds for past tensed truths. In the first (by Matthew Davidson), new arguments are provided to defend the idea that the presentist cannot adequately explain how what is now true about the past is grounded, since for the presentist the past is completely devoid of ontological ground. The second paper (by Brian Kierland) takes up the challenge of developing a presentist explanation of past truths, beginning by outlining some existing views in the literature before advancing an original proposal. (shrink)

This paper tries to clarify the logical structure of the relationship between labor values and prices from an axiomatic perspective. The famous “transformation problem” is interpreted as an impossibility result for a specific interpretation of value theory based on specific assumptions and definitions. A comprehensive review of recent literature is provided, which shows that there are various theoretically relevant and logically consistent alternative interpretations based on different assumptions and definitions.

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of (...) the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. (shrink)

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this “abundance of the future” is a non-adjunctive paraconsistent formalism based on subvaluations, (...) which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable (though both φ and ¬φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. (shrink)

Pretende-se nesse ensaio, analisar o conceito de temor a partir da perspectiva de Søren Kierkegaard e Hans Jonas, não necessariamente para estabelecer parâmetros interpretativos, mas para fomentar uma leitura a partir do episódio bíblico do sacrifício de Isaac por seu pai Abraão, neste texto interpretado a partir da heurística do temor, um conceito central da ética da responsabilidade proposta por Jonas como uma ética do futuro. Para tanto, analisaremos o temor como pathos existencial na filosofia kierkegaardiana, para destacar o aspecto (...) emocional que liga o conceito à autoridade parental na filosofia jonasiana e o conduz à hipótese de que é preciso “sacrificar” o presente em benefício do futuro. (shrink)

In this paper I start from a definition of “culture of the artificial” which might be stated by referring to the background of philosophical, methodological, pragmatical assumptions which characterizes the development of the information processing analysis of mental processes and of some trends in contemporary cognitive science: in a word, the development of AI as a candidate science of mind. The aim of this paper is to show how (with which plausibility and limitations) the discovery of the mentioned background might (...) be dated back to a period preceding the cybernetic era, the decade 1930–1940 at least. Therefore a somewhat detailed analysis of Hull's “robot approach” is given, as well as of some of its independent and future developments. -/- Reprinted in R.L. Chrisley (ed.), Artificial Intelligence: Critical Concepts in Cognitive Science, vol. 1, Routledge, London and New York, 2000, pp. 301-326. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...) to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the (...) variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras. (shrink)

O artigo se ocupa da Hermenêutica da facticidade, do filósofo alemão contemporâneo Martin Heidegger (1889-1976). Nosso propósito inicial é apresentar, sumariamente, os termos do referido projeto filosófico e como este pretende uma abordagem do fenômeno humano enfocado como “vida fática” (faktische Leben). Neste modo de visar, importa para Heidegger a determinação dessa vida, a qual ele denomina de “facticidade” (Faktizität), conceito que, ao longo de sua investigação, vai, progressivamente, ganhando importância e centralidade. Tratado no seio de Ontologia: Hermenêutica da Facticidade (...) (preleção do semestre de verão ministrada na Universidade de Friburgo em 1923), o conceito de facticidade tem lugar no tentame de elaboração de um modo de tornar nosso ser mais claro a nossa própria compreensão. Justamente por isso, uma tal hermenêutica de nós mesmos não constitui uma metodologia de interpretação de um objeto que pretensamente seríamos. Assim, hermenêutica diria, antes, do procedimento que, contando com a compreensão que temos de nosso próprio ser, pode tomar o sentido de nosso factum, de nosso fato de ser. Intentamos evidenciar o quanto a hermenêutica da facticidade é tão hermenêutica quanto também fenomenológica e que, a ideia de “tomar o nosso próprio ser nas mãos”. O artigo ainda se empenhará por deixar claro o quanto a facticidade não é um traço natural, substancial ou essencial do ente que somos; em sua caracterização fenomenológica, tal figura constitui, para Heidegger, uma dinâmica de “fazer-se”, o que nos leva a pensar no caráter em aberto e continuamente criador da vida em seu “dar-se”. Ao fim, ensaiamos, como nosso título anuncia, uma indicação do quanto a hermenêutica da facticidade teria a contribuir para o modo de compreender e comportar-se de uma psicologia fenomenológico-existencial. (shrink)

The interpretation of propositions in Lukasiewicz's infinite-valued calculus as answers in Ulam's game with lies--the Boolean case corresponding to the traditional Twenty Questions game--gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.

We aim to focus on the mimic gestures intentionally produced to be “monstrate” to others, thus attempting to propose a semiotic analysis on the actor’s face. We shall attempt to outline the extent to which, since the rise of cinema, the actor’s face has gained a foreground role as compared to the full-figured body, and the legacy of the nineteenth-century handbooks of scenic postures was crucial in this context, especially those of Antonio Morrocchesi and Alemanno Morelli. To deal with the (...) actor’s body as an instrument, means to make it a blank page to be used to re-design the character’s body, including the face. In this regard, it is worth mentioning the method of the pedagogue Jacques Lecoq—one of the greatest teachers of contemporary theatre—which consists in the use of a special mask during the training process: the so-called neutral mask. (shrink)

We propose expanding the authors’ shared novelty-seeking basis for creativity and curiosity by emphasizing an underlying computational principle: Minimizing prediction errors (mismatch between predictions and incoming data). Curiosity is tied to the anticipation of minimizing prediction errors through future, novel information, whereas creative AHA moments are connected to the actual minimization of prediction errors through current, novel information.

This paper extends the analysis of liberal principles in social choice recently proposed by Mariotti and Veneziani (2009a) to infinitely-lived societies. First, some novel characterisations of inegalitarian leximax social welfare relations are derived based on the Individual Benefit Principle (IBP), which incorporates a liberal, non-interfering view of society. This is surprising because the IBP does not explicitly incorporate any preference for inequality, nor does it assign priority to well-off members of society. Second, some impossibility results are derived that highlight a (...) general tension between standard fairness and efficiency axioms in social choice, and a liberal Principle of Non-Interference that generalises IBP. (shrink)

Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.

O propósito do artigo é abordar o conceito de jogo (Spiel) na hermenêutica filosófica de Gadamer, tal como aparece na obra Verdade e Método. Questionamos como o jogo, tratado como metáfora, nos permite compreender conceitos genuinamente hermenêuticos como compreensão e interpretação. O objetivo é mostrar o jogo como uma dinâmica existencial quando a questão é compreender e interpretar. Centramo-nos na noção de compreensão e no campo de jogo que a constitui; também, o quanto a interpretação é formada a partir de (...) estruturas de compreensão prévias e de significados historicamente consolidados. O objetivo, por fim, é indicar como seria engendrada a compreensão em um jogo que estabelece tanto o jogador quanto o jogado. Entre nossas metas específicas, cabe apontar que as interpretações nunca são cabais, estando, portanto, sujeitas a revisões de seus significados na própria dinâmica que os fundamenta. (shrink)

Let ${\mathbb{BRL}}$ denote the variety of commutative integral bounded residuated lattices (bounded residuated lattices for short). A Boolean retraction term for a subvariety ${\mathbb{V}}$ of ${\mathbb{BRL}}$ is a unary term t in the language of bounded residuated lattices such that for every ${{\bf A} \in \mathbb{V}, t^{A}}$ , the interpretation of the term on A, defines a retraction from A onto its Boolean skeleton B(A). It is shown that Boolean retraction terms are equationally definable, in the sense that there is (...) a variety ${\mathbb{V}_{t} \subsetneq \mathbb{BRL}}$ such that a variety ${\mathbb{V} \subsetneq \mathbb{BRL}}$ admits the unary term t as a Boolean retraction term if and only if ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ . Moreover, the equation s(x) = t(x) holds in ${\mathbb{V}_{s} \cap \mathbb{V}_{t}}$ . The radical of ${{\bf A} \in \mathbb{BRL}}$ , with the structure of an unbounded residuated lattice with the operations inherited from A expanded with a unary operation corresponding to double negation and a a binary operation defined in terms of the monoid product and the negation, is called the radical algebra of A. To each involutive variety ${\mathbb{V} \subseteq \mathbb{V}_{t}}$ is associated a variety ${\mathbb{V}^{r}}$ formed by the isomorphic copies of the radical algebras of the directly indecomposable algebras in ${\mathbb{V}}$ . Each free algebra in such ${\mathbb{V}}$ is representable as a weak Boolean product of directly indecomposable algebras over the Stone space of the free Boolean algebra with the same number of free generators, and the radical algebra of each directly indecomposable factor is a free algebra in the associated variety ${\mathbb{V}^{r}}$ , also with the same number of free generators.A hierarchy of subvarieties of ${\mathbb{BRL}}$ admitting Boolean retraction terms is exhibited. (shrink)